### Abstract

Previous investigations of riddling have focused on the case when the dynamical invariant set in the symmetric invariant manifold of the system is a chaotic attractor. A situation expected to arise commonly in physical systems, however, is that the dynamics in the invariant manifold is in a periodic window. We argue and demonstrate that riddling can be more pervasive in this case because it can occur regardless of whether the chaotic set in the invariant manifold is transversly stable or unstable. Scaling behavior associated with this type of riddling is analyzed and is supported by numerical experiments.

Original language | English |
---|---|

Pages (from-to) | 2926-2929 |

Number of pages | 4 |

Journal | Physical Review Letters |

Volume | 83 |

Issue number | 15 |

Publication status | Published - 11 Oct 1999 |

### Keywords

- COUPLED OSCILLATOR-SYSTEMS
- ATTRACTORS
- BASINS
- SYNCHRONIZATION
- BIFURCATIONS

### Cite this

*Physical Review Letters*,

*83*(15), 2926-2929.

**Riddling of chaotic sets in periodic windows.** / Lai, Y C ; Grebogi, C ; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 83, no. 15, pp. 2926-2929.

}

TY - JOUR

T1 - Riddling of chaotic sets in periodic windows

AU - Lai, Y C

AU - Grebogi, C

AU - Lai, Ying-Cheng

PY - 1999/10/11

Y1 - 1999/10/11

N2 - Previous investigations of riddling have focused on the case when the dynamical invariant set in the symmetric invariant manifold of the system is a chaotic attractor. A situation expected to arise commonly in physical systems, however, is that the dynamics in the invariant manifold is in a periodic window. We argue and demonstrate that riddling can be more pervasive in this case because it can occur regardless of whether the chaotic set in the invariant manifold is transversly stable or unstable. Scaling behavior associated with this type of riddling is analyzed and is supported by numerical experiments.

AB - Previous investigations of riddling have focused on the case when the dynamical invariant set in the symmetric invariant manifold of the system is a chaotic attractor. A situation expected to arise commonly in physical systems, however, is that the dynamics in the invariant manifold is in a periodic window. We argue and demonstrate that riddling can be more pervasive in this case because it can occur regardless of whether the chaotic set in the invariant manifold is transversly stable or unstable. Scaling behavior associated with this type of riddling is analyzed and is supported by numerical experiments.

KW - COUPLED OSCILLATOR-SYSTEMS

KW - ATTRACTORS

KW - BASINS

KW - SYNCHRONIZATION

KW - BIFURCATIONS

M3 - Article

VL - 83

SP - 2926

EP - 2929

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 15

ER -